I am currently working through a Greek composition course by myself, and I am a little confused by word order in even simple sentences. I understand that in word order is much less strict in Greek than in Latin (verbs don't have any need to come at the end of a sentence), and that it tends to reflect the emphasis of the sentence, however I am a little unsure about this sometimes.

For instance, I translated the sentence "The old man saw the goddess just before nightfall" as "ὁ γερων την θεαν ὑπο νυκτα εἰδεν". However, the answer key goes for "ὁ γερων εἰδε την θεαν ὑπο νυκτα". Is the translator simply putting emphasis on the "see" rather than some other form of interaction with the goddess (which seems unlikely to me), or is there something I'm missing?

For instance, I translated the sentence "The old man saw the goddess just before nightfall" as "ὁ γερων την θεαν ὑπο νυκτα εἰδεν". However, the answer key goes for "ὁ γερων εἰδε την θεαν ὑπο νυκτα". Is the translator simply putting emphasis on the "see" rather than some other form of interaction with the goddess (which seems unlikely to me), or is there something I'm missing?

Ancient Greek word order patterns (not rules) are dependent on genre, dialect and author.The answer-key word order looks suspiciously like English. A clause initial subject followed immediately by the main verb followed by the direct object is grammar textbook English syntax and by no means normal in ancient greek narrative. A common word order in Johannine narrative introducing speech (a narrative sub-genre) John 11:21a εἶπεν οὖν ἡ Μάρθα πρὸς τὸν Ἰησοῦν· John 4:21 λέγει αὐτῇ ὁ Ἰησοῦς· πίστευέ μοι, γύναι, ὅτι ἔρχεται ὥρα ... Note that the subject follows the main verb and the person spoken to may precede the subject.

Sophocles likes to pile up modifiers in front of substantives and nouns. Here is an example from Aeschylus Agamemnon. This is also a species of speech introduction (oratio obliqua, metaphorical).

A.Ag 494b-495μαρτυρεῖ δέ μοι κάσιςπηλοῦ ξύνουρος διψία κόνις τάδε ...

The subject here is κόνις (dust) which arrives rather late in the clause. Note the clause initial main verb μαρτυρεῖ (bear witness) followed by the the person spoken to μοι. The string of modifiers διψία (thirsty) and κάσις πηλοῦ ξύνουρος “twin-sister of mud” (LSJ); all of these modifiers are piled up in front of the noun κόνις they modify. Sophocles does this a lot.

Clause initial main verbs are not anything like a rule. But some analysts of Koine consider any substantive fronted (left of the main verb) to be highlighted (increased salience). This is a very complex question. Certain constituents are regularly found before the main verb, for example genitive absolutes which serve as contextualizers in narrative are often clause initial.

I'm working through Sidwick's compositions, and am also struggling with word order.

I found the introduction to Exercises in some of the more difficult principles of Greek syntax, by James Robinson Boise to be helpful. (Download-able from Google Books) This 7-page section is titled "Arrangement of Words in an Attic Prose Sentence." In brief, the order of a simple sentence is Subject - Remote Object - Nearer Object - Verb. From there, Boise develops it quite a bit, bringing in adverbs and subordinate clauses. He also presents what he calls "Inverted Order," which .. just that! He also emphasizes that the first and last position in a sentence (clause) are the places of emphasis.

Following Boise's concepts, I'm usually able to come close to Sidgwick's answer key. Sidgwick's recommendations on word order are much less specific; "Words should be in their natural order." Not too helpful for a native English speaker who is new to Greek, but after a while, after lots of reading and some composition, one gets a sense for what "natural order" was, to Sidgwick and the ancient Greeks.